论文标题
同型路径代数
Homotopy Path Algebras
论文作者
论文摘要
我们定义了一个基本的代数类别，我们称之为同型路径代数。我们发现，这样的代数始终接受细胞分辨率，并详细介绍了这些代数之间的亲密关系，拓扑空间的分层以及入口/出口路径。作为示例，我们证明了由于粘合品品种的粘结量引起的同源镜像对称性，并且由于berglund-hübsch-krawitz用于具有最大对称性的超丘角。我们还证明了一种可撒性的形式意味着koszulity和最小的细胞分辨率的存在。特别是，当由曲曲面的弗罗贝尼乌斯形态的图像确定的代数是可引导的时，它是koszul并接受最小的细胞分辨率。
We define a basic class of algebras which we call homotopy path algebras. We find that such algebras always admit a cellular resolution and detail the intimate relationship between these algebras, stratifications of topological spaces, and entrance/exit paths. As examples, we prove versions of homological mirror symmetry due to Bondal-Ruan for toric varieties and due to Berglund-Hübsch-Krawitz for hypersurfaces with maximal symmetry. We also demonstrate that a form of shellability implies Koszulity and the existence of a minimal cellular resolution. In particular, when the algebra determined by the image of the toric Frobenius morphism is directable, then it is Koszul and admits a minimal cellular resolution.
